Fuzzy K-means clustering with reconstructed information

Clustering techniques play a pivotal role in unveiling the inherent structure of unlabeled data. When dealing with overlapping clusters, traditional hard clustering methods encounter challenges. As a representative of soft clustering methods, Fuzzy K-Means (FKM) enables data points to be assigned different degrees of membership to multiple clusters, offering a solution to this problem. However, when dealing with high-dimensional data, the performance of FKM is often affected by redundant features and noise. To address this limitation, this paper introduces a Fuzzy K-Means Clustering with Reconstructed Information (FKMRI) method. This method combines the reconstruction term with a cluster weight variable to effectively capture the true nature of data structure, thereby enhancing the clustering capability of FKM in high-dimensional spaces. We theoretically analyze the convergence of the FKMRI algorithm and prove its time complexity to be \(O\left( (c+P(c)) n d^2+c n d\right)\) $O\left((c+P(c)),n,d^2,+,c,n,d\right)$ . Finally, we evaluate the performance of FKMRI on standard benchmark datasets including Yale-32x32, Yale-64x64, ORL-32x32, and ORL-64x64. The results demonstrate that, in comparison to five current state-of-the-art algorithms (K-Means, FKM, Kernel-km, RSFKM, DFKM), FKMRI exhibits an average improvement of over 18% in terms of accuracy rate (ACC) and normalized mutual information (NMI). These findings convincingly validate the effectiveness and efficiency of the proposed algorithm in handling high-dimensional data clustering, providing valuable support for related research fields.